How to link two different physics objects together?
All you need to make the cloth more stiff in one area and leave the rest of the cloth less stiff, is to create a vertex group, and assign desired scale of each vertex in this group (0.0 .. 1.0). It's better to do it with weight painting mode. Then you just set this group as stiffness scale factor map. See pictures below.



Anywhere you see those vertex group selector, you can do it on per-vertex basis.